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FOCS
2004
IEEE
13 years 11 months ago
Hardness of Approximating the Shortest Vector Problem in Lattices
Let p > 1 be any fixed real. We show that assuming NP RP, there is no polynomial time algorithm that approximates the Shortest Vector Problem (SVP) in p norm within a constant ...
Subhash Khot
STOC
2007
ACM
83views Algorithms» more  STOC 2007»
14 years 8 months ago
Lattices that admit logarithmic worst-case to average-case connection factors
We demonstrate an average-case problem that is as hard as finding (n)-approximate shortest vectors in certain n-dimensional lattices in the worst case, where (n) = O( log n). The...
Chris Peikert, Alon Rosen
ECCV
2006
Springer
14 years 9 months ago
Discovering Texture Regularity as a Higher-Order Correspondence Problem
Abstract. Understanding texture regularity in real images is a challenging computer vision task. We propose a higher-order feature matching algorithm to discover the lattices of ne...
James Hays, Marius Leordeanu, Alexei A. Efros, Yan...
CORR
2010
Springer
178views Education» more  CORR 2010»
13 years 6 months ago
Enumerative Algorithms for the Shortest and Closest Lattice Vector Problems in Any Norm via M-Ellipsoid Coverings
We give an algorithm for solving the exact Shortest Vector Problem in n-dimensional lattices, in any norm, in deterministic 2O(n) time (and space), given poly(n)-sized advice that...
Daniel Dadush, Chris Peikert, Santosh Vempala
CRYPTO
1997
Springer
207views Cryptology» more  CRYPTO 1997»
13 years 12 months ago
Public-Key Cryptosystems from Lattice Reduction Problems
We present a new proposal for a trapdoor one-way function, from which we derive public-key encryption and digital signatures. The security of the new construction is based on the ...
Oded Goldreich, Shafi Goldwasser, Shai Halevi